Research efforts have been conducted to study the economic performance of a decarbonized steel industry. In (Boldrini et al., 2022), A. Boldirini et al. formulated a model of an exemplary steel plant. Then, after utilizing a historic time series of electricity from the Dutch day-ahead market, a linear programming problem was solved to minimize the cost of the plant’s electricity consumption. This provides insight into the market price’s influence on the plant’s operation. Other research efforts focused on creating models with a higher level of detail. A. Kruger et al. studied the economics of iron ore reduction with hydrogen using water electrolysis technologies. The authors considered different electrolysis technologies. The sensitivity of the process economics to the electrolyzer’s capital expenditure (CAPEX) and electricity costs was then analyzed (Krüger et al., 2020). X. Zang et al. studied the operation of a steel plant that is composed of four main processes (Zhang et al., 2016). The scheduling problem was created using resource task network modeling. This method enabled the application of operational constraints between each of the four processes. The high level of detail in this resulted in a high computational cost. The potential of industrial demand response was studied for other industries. In (Sofana Reka and Ramesh, 2016), the authors studied the demand response of a refinery using the resource network modeling approach. S. Valera et al. investigated the scheduling of alkaline water electrolysis for power-to-X applications (Varela et al., 2021). Researchers used a data-driven approach to analyze the scheduling of an air separation unit in (Tsay et al., 2019).

On the other hand, some researchers focused on implementing aggregate models to study the influence of flexibility. An available flexible industrial demand model is characterized by two terms: α , T proc . The first term, ranging between 0 and 1, represents the extent of industrial demand flexibility. The second term, denoted as the process horizon, is used as a time horizon to ensure that the industrial demand redistribution is energy neutral. Other modeling choices were also explored (Papadaskalopoulos et al., 2018). Another approach to representing industrial demand is to divide it into three options. The flexible demand option allows customers to reschedule their demand within operational constraints. The second option is on-site generation, where the customer can run their on-site backup generator. The final option is energy storage, where the customer purchases and stores energy during periods of low prices (Angizeh et al., 2019).

It can be concluded that the two modeling approaches serve different purposes. The high-level approach examines the operational challenges of flexible energy consumption and the potential benefits from the plant’s perspective, assuming the market price is given. In contrast, low-level models are used to explore the benefits at the system level without considering the constraints imposed by the plant’s dynamics. This review shows that modeling with a moderate level of detail has not been addressed. This level would enable us to optimize investment in flexibility capacities, consider the impact of demand response on the energy market, and provide a representation of scheduled hydrogen flows that meet the hydrogen demand.

Aside from single-point optimization, performing a near-optimal analysis helps provide a better understanding of solution behavior. In the near-optimal analysis, the objective function value is allowed to deviate from the optimal value within a defined range, known as the optimality gap. This variation enables us to explore different optimization paths, or different sets of optimization variables that result in a near-optimal result. This practice is common in energy system analysis, especially when studying energy storage and flexibility (Pedersen et al., 2021; Teo et al., 2018; Pandzic et al., 2015; Neumann and Brown, 2021; Grochowicz et al., 2023). In addition, modeling to generate alternatives is used to examine the influence of different design and policy choices for energy system analysis (Lombardi et al., 2020; Lombardi et al., 2023). This is due to the shortcomings of optimal solution analysis, including the imperfect representation of the mathematical models, the variability of problem constraints (such as fuel costs and weather conditions), and the lack of information on the solution’s robustness (Voll et al., 2015).

What appears to be missing in the literature is a systematic study of the impact of power system parameters on the trade-offs between flexibility options for hydrogen production and a method that is not sensitive to small variations in problem settings. In this research, near-optimal analysis is employed to explore various options for near-optimal electrolysis and storage capacities, as well as near-optimal investment options.

The purpose of this research is to investigate the interactions between large energy consumers and the power system. Mainly, the focus is on the optimal investment and how it responds to variations in the problem variables. The analysis results are relevant to both industry and energy system planners.

Figure 1 describes the model used for this paper. The two shaded rectangles represent the two main components of the model: the power system, depicted in blue, and the hydrogen flow, shown in green. The electrolysis plant is a common component of the two parts: its level of operation influences electricity prices and determines the quantity of hydrogen that can be generated, stored, or fed directly to the reduction process. Additionally, the model takes into account the energy required for hydrogen compression during storage. This model is used to run an optimization problem that minimizes the system cost. The system cost is composed of two components: the generation cost of the power plants and the annualized costs of investment in the hydrogen facilities. This enables us to investigate the impact of variables on the optimal hydrogen capacities. In other words, how do the CAPEX of electrolysis and storage, the natural gas price, the carbon emission price, or the renewable capacities impact the optimal investments in electrolysis and storage capacities?

This paper presents the development of a model of an optimization problem that couples the operation of the power system with a large flexible energy consumer. This enables us to examine the impact of the exhibited flexibility on the energy market. In addition, to understand the interactions among the optimization problem variables, this paper includes an analysis of the interactions between the power system variables and the optimal capacities for storage and electrolysis. Finally, in this paper, the convexity attribute of the linear optimization problem is utilized to map the near-optimal regions. The mapping process has two merits. The first merit is that it allows for a better understanding of the problem solution. The shape of the region describes the implicit relation between the two capacities, storage and electrolysis. In addition, the application of near-optimal region mapping provides enhanced insight into the sensitivity of optimal capacities with respect to problem variables. Instead of conducting sensitivity analyses on the optimal capacity points, the study of variations in the near-optimal region generates an extended sensitivity analysis.

Equation 2 presents an energy balance constraint. The total energy generated by all conventional generation units P g , t and renewable resources P res,t is equal to the sum of the national electricity demand D E , electrolysis power consumption P E , t , and hydrogen compression energy consumption P s , t for every hour t . ∑ g = 1 g = G P g , t + P res,t = D E + P E , t + P s , t ∀ t (2)

In addition to energy conservation, the energy generated by every P g , t unit is limited to the unit’s capacity K g (Equation 3). In Equation 4, the renewable generation P res,t is bounded by the product of the installed renewable energy capacity K res and the hourly capacity factor C F res,t . 0 ≤ P g , t ≤ K g ∀ g , t (3) 0 ≤ P res,t ≤ C F res,t ⋅ K res ∀ t (4)

The upper and lower bounds, L B ⋅ K and U B ⋅ K , of the electrolysis power consumption P E , t and the storage operating level S l , t are defined in Equations 5, 6. L B S ⋅ K S ≤ S l , t ≤ U B S ⋅ K S ∀ t (5) L B E ⋅ K E ≤ P E , t ≤ U B E ⋅ K E ∀ t (6)

Assuming a constant electrolysis efficiency η E , the total amount of hydrogen generated at any given hour G H 2 , t is defined as shown in Equation 7. G H 2 , t = η E ⋅ P E , t ∀ t (7)

The excess generated hydrogen can be stored in the storage facility at any time step. In order to store hydrogen, energy is required for compression. Equation 8 describes the energy needed to compress hydrogen P s , t is a function of the storage efficiency η S and the hydrogen inflow rate to the storage tank F H 2 , i n , t . P s , t = 1 − η S ⋅ F H 2 , i n , t / η E ∀ t (8)

In addition, mass conservation equations applied to the hydrogen storage facility are described in Equation 9. The change in the hourly storage level S l , t is the integration of the difference between hydrogen inflow F H 2 , i n , t and outflow F H 2 , o u t , t rates. S l , t + 1 − S l , t = Δ t ⋅ F H 2 , i n , t − F H 2 , o u t , t ∀ t (9)

This part of the model relates the hydrogen inflow rate to the storage and electrolysis facilities to the considered hydrogen demand. Two scenarios are considered for the hydrogen demand. In scenario one, the steel plant is assumed to operate constantly throughout the year. Therefore, as shown in Equation 10, the hydrogen demand D ̄ H 2 equals the hydrogen produced by the electrolyzer minus the inflow to the storage tank, plus the outflow from the storage tank. D ̄ H 2 = G H 2 , t − F H 2 , i n , t + F H 2 , o u t , t ∀ t (10)

In scenario two, another source of flexibility, operational flexibility, is considered. In this context, operational flexibility is defined as the ability to vary the consumption of hydrogen on an hourly basis. This requires overcapacity of the plant facility.

In this scenario, the capacity of the industrial plant is assumed to be oversized by a factor of 1 + α . Therefore, the hourly hydrogen demand D H 2 , t can vary under the condition of meeting hydrogen demand quota over a defined time period, called a flexibility period d . The hydrogen hourly demand equations can be expressed as with Equations 11, 12: D H 2 , t = G H 2 , t − F H 2 , i n , t + F H 2 , o u t , t ∀ t (11) ∑ t = 1 t = d Δ t ⋅ D H 2 , t = D ̄ H 2 ⋅ d / Δ t (12)

The flexible consumption can vary between the upper and lower bounds that depend on the over-sizing factor α , see Equation 13. Note that as the oversizing coefficient increases, the lower bound of consumption increases too. L B D ⋅ 1 + α ⋅ D ̄ H 2 ≤ D H 2 , t ≤ 1 + α ⋅ D ̄ H 2 ∀ t (13)

In this subsection, the influence of storage and electrolysis CAPEX on the optimal capacities is studied. Figure 5 illustrates the variation of near-optimal regions as the CAPEX of storage and electrolysis vary between 50% and 150% of the original value. The first observation is that the near-optimal regions are larger in both cases for smaller CAPEX. This can be expected as smaller CAPEX implies a smaller contribution of investment costs to the overall costs. Thus, the optimum becomes even shallower. In addition, while the variation in storage CAPEX significantly influences the optimal storage capacity, it appears to have a much smaller effect on the optimal electrolysis capacity. In contrast, the variation of electrolysis CAPEX significantly influences both capacities. In other words, higher electrolysis capacity necessitates more storage, but it is not the same in the other direction. This is primarily because the cost of investing in storage is much smaller than the cost of investing in electrolysis, with a ratio of 1:25. The effect of this ratio can be recognized if we compare the variation of the levelized cost of hydrogen LCOH in both cases. While the increase in storage CAPEX raises the LCOH from 5.976 to 6.004 €/kg, the increase in electrolysis CAPEX raises the LCOH from 5.428 to 6.371 €/kg.

Another essential factor that can influence the optimal hydrogen capacities is the renewable energy penetration in the power system. Figure 6 illustrates the variation of the regions as the additional capacities of solar and wind energy sources vary from 0 to 10 GW. Both graphs show a general trend of higher investment in flexibility for larger renewable energy capacities. Nonetheless, the increase in storage capacity is significantly larger than the increase in electrolysis capacity. Another similarity between the two graphs is that at + 10 GW, the electrolysis capacity declines, and the storage capacity increases. This is due to the high CAPEX of electrolysis. In addition, as renewable capacities increase, there will be more instances of excess renewable energy, allowing storage to be filled at a slower rate. Note that the electrolysis capacity required to directly supply the hydrogen demand is 1925 MW.

The primary difference between the two graphs is that the solar energy case favors a larger electrolysis capacity and substantially smaller storage capacity compared to the wind energy case. This is expected when comparing the generation profiles of both technologies. Although solar energy generation varies throughout the year, the main variation occurs on a daily basis. This sharp variation in abundant solar energy aligns the larger electrolysis capacity to utilize the peak and a smaller storage capacity, which is still sufficient to cover the intraday variation. On the other hand, a larger timescale of wind energy variation results in a larger storage capacity and a smaller electrolysis capacity. The additional renewable energy capacities reduce the average cost of energy generation in the system. Thus, the contribution of the investment cost to the total cost increases. In the initial case, the investment costs accounted for 16% of the total cost. This contribution increases to 32.1% in the case of +10 GW solar and 42.5% in the case of +10 GW wind. This high contribution leads to a sharper optimum and thus a smaller near-optimal region. The LCOH decreases from 5.991 €/kg in the initial case to 4.633 €/kg for +10 GW solar and 3.526 €/kg for +10 GW wind.

The carbon-emitting generation technologies, natural gas and coal, play a crucial role in the economics of the power system. Therefore, studying their influence on optimal investment should provide relevant insight. The natural gas price variation is considered because of its recent volatility. In addition, the carbon emission price is considered due to its impact on the generation costs and the merit order. Figure 7 shows the variation of the near-optimal regions for a set of natural gas and carbon emission prices.

The growth of storage and electrolysis capacities in response to increasing natural gas prices can be observed. However, the influence of the carbon emission price is not as straightforward as that of gas. To analyze this behavior, we will focus first on the variation of the regions’ centers. This variation indicates that the system favors higher investment in flexibility assets for both smaller and larger carbon emission prices. In its essence, the flexibility would save costs as it allows for load shifts from high-price instances to low-price instances. If we refer to Figure 8, and more specifically to the merit order, we can observe a plateau in the merit order between the prices 120–150 €/kWh. This is because, for the initial natural gas and carbon emission prices, the generation costs of coal and some of the natural gas units are too close. Knowing that coal emits a much higher quantity of carbon dioxide per MWh, any increase or decrease in the carbon emission price leads to a gap between the coal and natural gas units, and therefore, to more potential benefits of flexibility. A final note is that the LCOH is more sensitive to natural gas prices, as it varies from 4.339 to 6.908 €/kg, than to carbon emission prices, which vary from 5.098 to 6.789 €/kg.